In optical communication systems that employ coherent optical receivers, the modulated optical signal received at the coherent receiver is mixed with a narrow-line-width local oscillator (LO) signal, and the combined signal is made incident on one or more photodetectors. The frequency spectrum of the electrical current appearing at the photodetector output(s) is substantially proportional to the convolution of the received optical signal and the local oscillator (LO), and contains a signal component lying at an intermediate frequency that contains data modulated onto the received signal. Consequently, this “data component” can be isolated and detected by electronically filtering and processing the photodetector output current.
The LO signal is typically produced using a semiconductor laser, which is typically designed to have a frequency that closely matches the frequency of the laser producing the carrier signal at the transmitter. However, as is known in the art, such semiconductor lasers exhibit a finite line width from non-zero phase noise. As a result, frequency transients as high as ±400 MHz at rates of up to 50 kHz are common. This frequency offset creates an unbounded linear ramp in the phase difference between the two lasers. In addition, many such lasers often exhibit a line width of the order of 1 MHz with a Lorentzian spectral shape. As a result, even if the transmitter and LO lasers were to operate at exactly the same average frequency, a phase error linewidth of about ±2 MHz can still exist. This Lorentzian spectrum creates a phase variance that grows linearly with time, and the initial phase difference is random, so over the lifetime of operation of the optical connection the phase error is unbounded.
As is known in the art, data is typically encoded in accordance with a selected encoding scheme (e.g. Binary Phase Shift Keying (BPSK); Quadrature Phase Shift Keying (QPSK), 16-Quadrature Amplitude Modulation (16-QAM) etc.) to produce symbols having predetermined amplitude and phase. These symbols are then modulated onto an optical carrier for transmission through the optical communications system to a receiver. At the receiver, the received optical signal is processed to determine the most likely value of each transmitted symbol, so as to recover the original data.
As is known in the art, a frequency mismatch or offset Δf, and independent phase noise between the transmitter and LO laser appears as a time-varying phase θ of the detected symbols, relative to the phase space of the applicable encoding scheme. This variation of the symbol phase θ is exacerbated by phase non-linearities of the optical communications system, and in particular, cross-phase modulation (XPM). The symbol phase θ is unbounded, in that it tends to follow a random-walk trajectory and can rise to effectively infinite multiples of 2π. Because the symbol phase θ is unbounded, it cannot be compensated by a bounded filtering function. However, unbounded filtering functions are susceptible to cycle slips and symbol errors, as will be described in greater detail below.
Applicant's U.S. Pat. No. 7,606,498 entitled Carrier Recovery in a Coherent Optical Receiver, which issued Oct. 20, 2009, teaches techniques for detecting symbols in the presence of a frequency mismatch between the received carrier (that is, the transmitter) and the LO laser. The entire content of U.S. Pat. No. 7,606,498 is incorporated herein by reference. In the system of U.S. Pat. No. 7,606,498, an inbound optical signal is received through an optical link 2, split into orthogonal polarizations by a Polarization Beam Splitter 4, and then mixed with a Local Oscillator (LO) signal by a conventional 90° hybrid 8. The composite optical signals emerging from the optical hybrid 8 are supplied to respective photodetectors 10, which generate corresponding analog signals. The analog photodetector signals are sampled by respective Analog-to-Digital (A/D) converters 12 to yield multi-bit digital sample streams corresponding to In-phase (I) and Quadrature (Q) components of each of the received polarizations.
The format and periodicity of the SYNC bursts may conveniently be selected as described in U.S. Pat. No. 7,606,498. In each of the embodiments illustrated in FIGS. 2A and 2B, the optical signal includes nominally regularly spaced SYNC bursts 14 embedded within a stream of data symbols 16. Each SYNC burst 14 has a respective predetermined symbol sequence on each transmitted polarization. In the embodiment of FIG. 2A, two orthogonal symbol sequences are used in each SYNC burst 14; each symbol sequence being assigned to a respective transmitted polarization. FIG. 2B illustrates an alternative arrangement, in which each of the I and Q components of each transmitted polarization is assigned a respective orthogonal symbol sequence.
Returning to FIG. 1, from the A/D converter 12 block, the I and Q sample streams of each received polarization are supplied to a respective dispersion compensator 18, which operates on the sample stream(s) to compensate chromatic dispersion. The dispersion-compensated sample streams appearing at the output of the dispersion compensators 18 are then supplied to a polarization compensator 20 which operates to compensate polarization effects, and thereby de-convolve transmitted symbols from the complex sample streams output from the dispersion compensators 18. If desired, the polarization compensator 20 may operate as described in Applicant's U.S. Pat. No. 7,555,227 which issued Jun. 30, 2009. The entire content of U.S. Pat. No. 7,555,227 is incorporated herein by reference. The polarization compensator 20 outputs complex-valued symbol estimates X′(n) and Y′(n) of the symbols transmitted on each polarization. These symbol estimates include phase error due to the frequency offset Δf between the Tx and LO frequencies, laser line width and Cross-phase modulation (XPM). The symbol estimates X′(n) and Y′(n) are supplied to a carrier recovery block 26 (see FIG. 1), which performs carrier recovery and phase error correction, and symbol determination. Two known carrier recovery and symbol determination techniques are described below.
In the system of U.S. Pat. No. 7,606,498 each SYNC burst is used to determine an initial phase error value γ0, which is used to calculate an initial phase rotation κ0 for the start of processing the next block of data symbols. Once the SYNC burst has been processed, the receiver switches to a data directed mode, during which the phase rotation is updated at predetermined intervals and applied to successive data symbol estimates X′(n) and Y′(n) to produce corresponding rotated data symbol estimates X′(n)e−jκ(n) and Y′(n)e−jκ(n). The decision value X(n), Y(n) of each transmitted symbol can be determined by identifying the decision region in which the rotated symbol estimate lies, and the symbol phase error γ calculated and used to update the phase rotation.
Applicant's U.S. Pat. No. 8,315,528 which issued Nov. 20, 2012 teaches a zero-mean carrier recovery technique in which two or more SYNC bursts are processed to derive an estimate of a phase slope ψ indicative of the frequency offset Δf between the transmit laser and the Local Oscillator (LO) of the receiver. The phase slope ψ is then used to compute a phase rotation κ(n) which is applied to each symbol estimate X′(n), Y′(n) to produce corresponding rotated data symbol estimates X′(n)e−jκ(n), Y′(n)e−jκ(n) which can then be filtered to remove XPM and find the decision values X(n), Y(n) of each transmitted data symbol. The entire content of U.S. Pat. No. 8,315,528 is incorporated herein by reference.
The processes described in U.S. Pat. Nos. 7,606,498 and 8,315,528 are unbounded, and thus can compensate unbounded symbol phase κ. However, both of these techniques assume that each rotated symbol estimate X′(n)e−jκ(n) and Y′(n)e−jκ(n) lies in the correct decision region of the symbol phase space. This means that when the symbol phase error γ becomes large enough (e.g. ≥π/4 for QPSK, or ≥π/2 for BPSK) the rotated symbol estimate will be erroneously interpreted as lying in a decision region that is adjacent to the correct decision region. When this occurs in respect of an isolated symbol estimate, the resulting “symbol error” will be limited to the affected symbol. On the other hand, where a significant number of symbol errors occur in succession, the receiver may incorrectly determine that a “cycle-slip” has occurred, and reset its carrier phase to “correct” the problem. Conversely, the receiver may also fail to detect a cycle slip that has actually occurred. This can result in the erroneous interpretation of a large number of symbols. FIGS. 3A and 3B illustrate this problem.
FIG. 3A illustrates a Quadrature Phase Shift Keying (QPSK) symbol constellation comprising four symbols (A-D) symmetrically disposed in a Cartesian symbol space defined by Real (Re) and Imaginary (Im) axes. In the symbol space of FIG. 3A, each quadrant corresponds with a decision region used for determining the respective decision value for each rotated symbol estimate. A rotated symbol estimate 28 is a complex value composed of Real and Imaginary components, which can therefore be mapped to the symbol space, as may be seen in FIG. 3A. It is also convenient to represent the rotated symbol estimate 28 as a polar coordinate vector having a phase θ and magnitude M, as shown in FIG. 3A.
As may be seen in FIG. 3A, the assumption that the rotated data symbol 28 estimate lies in the correct decision region means that the symbol phase error γ is calculated as the angle between the rotated data symbol estimate 28 and the nearest symbol of the encoding scheme (symbol B in FIG. 3A). As may be seen in FIG. 3B, the calculated phase error γ is zero when the phase θ corresponds with a symbol of the constellation, and increases linearly as the phase θ approaches a boundary between two decision regions. However, as the phase θ crosses a decision boundary (at θ=0, ±π/2, and ±π in FIGS. 3A and 3B), there is a discontinuity in the calculated phase error γ. For example, as the phase θ increases through the decision boundary at π/2, the calculated phase error γ reaches +π/4, and then jumps to −π/4, which is π/2 away from the correct phase error. This discontinuity increases the probability of making subsequent symbol errors, and can contribute to the occurrence of cycle slips. Once a cycle slip has occurred, subsequently received symbols will be incorrectly decoded until the problem has been detected and rectified.
An alternative frequency and phase estimation technique known in the art is the Viterbi-Viterbi algorithm, in which the Cartesian coordinate symbol estimates X′(n) and Y′(n) are raised to the fourth power to determine the phase rotation value that has the greatest probability of occurring and then these values are filtered using Cartesian averaging. The resulting phase rotation is then divided by four and applied to the received samples to try to determine the most likely decision values X(n), Y(n) of each transmitted data symbol. This approach suffers a limitation in that dividing the phase estimate by four also divides the 2π phase ambiguity by four, meaning that if incorrectly resolved this ambiguity causes a π/2 cycle slip. This technique can provide satisfactory performance in cases where the phase errors are dominated by a small frequency offset between the TX and LO lasers and moderate laser line widths. However, in the presence of XPM, this approach becomes highly vulnerable to producing cycle slips.
In some cases, the above-noted problems can be mitigated by use of a sufficiently strong Forward Error Correction (FEC) encoding scheme, but only at a cost of increased overhead, which is undesirable.
Techniques for carrier recovery that overcome limitations of the prior art remain highly desirable.